After more than three years of watching its relentless ascent, Londoners could be forgiven for failing to have registered that on March 30, the Shard finally stopped growing. The last piece of steel was fitted to the tower’s crown by a trio of site operatives known to history as Daz, G-man and Mr B, bringing it to a height of 309.6768 metres – a figure that varies ever so slightly in response to changes in temperature.

That is a full 75 metres taller than One Canada Square, the tower at London’s Canary Wharf that has been Britain’s tallest since its completion in 1991. When work on the Shard finishes at the beginning of next year it will not only claim that title but that of tallest building across the entire European Union.

Unsurprisingly, given its prominence, few recent buildings have proved more divisive. For its fans, the Shard is a statement of London’s confidence – of the fact that this ancient city has now grown into a thrusting metropolis, unburdened by its past, and with nothing to fear from the likes of Frankfurt and Shanghai. They argue, too, that there is much that is remarkable about the design beyond the matter of its height.

Love it or loathe it, that certainly is true. It is the work of the Italian architect Renzo Piano, perhaps best known for designing Paris’s stridently mechanistic Pompidou Centre with his former partner, Richard Rogers. The Shard, however, belongs to a different tradition of modern architecture – one that draws its imagery not from industry but from the organic world.

In the early decades of the last century, a group of German architects, centred on the utopian visionary Bruno Taut, became enamoured by the idea of directing new developments in glass technology towards the creation of buildings of crystalline form and often gargantuan scale.

They built almost nothing, but schemes such as Taut’s fantastical proposal of 1919 to create a city in the Alps constructed entirely of glass continue to resonate in the imaginations of architects today. The sparkling, craggy spire that now looms over London Bridge station could have been plucked straight from one of Taut’s expressionistic watercolours.

The fact that the Shard’s footprint shrinks from floor to floor has major implications not only for its appearance but for its organisation, too. Different sizes of floor invite different uses. The bottom third of the building – where the floors are broadest – happily accommodates office space, but above that restaurants, a hotel, a spa, and some of London’s most desirable apartments are being slotted in. The public viewing gallery at the very top is expected to attract more than two million visitors each year. While Piano’s claim that the Shard is not a tower but “a vertical city” might smack of hyperbole, it is undeniable that in its mix of uses, his building differs radically from any built in the UK before.

Yet many Londoners are unpersuaded that their city has been best served by the addition of such a domineering structure. At the 2002 planning inquiry into the project, English Heritage, the Royal Parks Foundation and a raft of London boroughs lined up to object. Their doubts centred not just on the building’s height but on its location. From the 1970s until very recently, the construction of tall buildings in London was restricted to its two primary business districts, the City and Canary Wharf, where their visual impact could be contained. Sited in near isolation on the south bank of the Thames, the Shard is one of the first examples of a new generation of towers that depart from this cluster model. We would have seen more already had it not been for the economic downturn. However, the number of extant planning permissions for very tall buildings all across the capital suggests that its skyline could be transformed beyond recognition very soon.

The causes of this dramatic shift can be traced back to the election of Ken Livingstone as the city’s mayor in 2000. One of his first actions was to tell the capital’s boroughs that he had “no objection in principle to London having the tallest of buildings”. With the publication of the London Plan two years later, he effectively denied them the right to impose blanket height restrictions, overnight transforming the sky above the capital into gold-rush territory. As long as the developers’ proposals didn’t endanger aircraft or obscure protected views of the Houses of Parliament and St Paul’s Cathedral, they found they could build pretty much as high as they wanted.

The south bank of the Thames, where the Shard stands, is particularly vulnerable to the effects of this liberalisation. A line of very tall – largely residential – buildings is now planned for sites extending all the way from Vauxhall in the West to Deptford in the East. Given London’s housing shortage, there are good reasons to welcome that escalation in height. However, what both Livingstone and the current mayor, Boris Johnson, have failed to provide is a plan that might steer all this development to a considered outcome.

The Shard may stand alone today, but what will it look like when hemmed in by such soon-to-arrive neighbours as the Boomerang and the Quill? In the absence of a vision to which London’s skyline might aspire, the city is at risk of transforming its riverside into a Costa del Icon, along which every tower is competing to be taller and more flamboyant than the next.

The Shard may be as impressive a skyscraper as any being built in the world today, but it suggests worrying questions about the direction that London is heading in. With the mayoral election now less than a month away, it might now be a good time for Londoners to start asking them.